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Simplify \(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)

Mathematics
JAMB 1986

Simplify \(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
  • A. \(\frac{2x}{(x - 2)(x + 2)(x^2 - 4)}\)
  • B. \(\frac{2x}{x^2 - 4}\)
  • C. \(\frac{x}{x^2 - 4}\)
  • D. \(\frac{4x}{x^2 - 4}\)
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Correct Answer: Option D
Explanation
\(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)

= \(\frac{(x + 2) + (x - 2) + 2x}{(x + 2)(x - 2)}\)

= \(\frac{4x}{x^2 - 4}\)

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